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The value of $$\begin{vmatrix} 1 & \log _x y & \log_x z \\ \log _y x & 1 & \log_y z \\ \log _z x & \log _z y & 1 \end{vmatrix}$$ is

  1. $0$
  2. $1$
  3. $-1$
  4. None of these
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3 Answers

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First row: logx/logx , logy/logx , logz/logx. Take 1/logx out then frist row will be logx , logy, logz

Similarly second and third row will become logx , logy . logz.

As two rows are identical, so determinant =0
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Put x=y=z so answer is ZERO
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anyway  solve you get answer = 0 which is option A

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